Mean and variance of coincidence counting with deadtime

We analyze the first and second moments of the coincidence-counting process for a system affected by paralyzable (extendable) deadtime with (possibly unequal) deadtimes in each singles channel. We consider both “accidental” and “genuine” coincidences, and derive exact analytical expressions for the first and second moments of the number of recorded coincidence events under various scenarios. The results include an exact form for the coincidence rate under the combined effects of decay, background, and deadtime. The analysis confirms that coincidence counts are not exactly Poisson, but suggests that the Poisson statistical model that is used for positron emission tomography image reconstruction is a reasonable approximation since the mean and variance are nearly equal.